doping dependence of spin excitations and its …superconductivity in iron pnictides, we study...

ARTICLE

Received 13 May 2013 | Accepted 5 Nov 2013 | Published 4 Dec 2013

Doping dependence of spin excitations andits correlations with high-temperaturesuperconductivity in iron pnictidesMeng Wang1,*, Chenglin Zhang2,3,*, Xingye Lu1,3,*, Guotai Tan3, Huiqian Luo1, Yu Song2,3,

Miaoyin Wang3, Xiaotian Zhang1, E.A. Goremychkin4, T.G. Perring4, T.A. Maier5, Zhiping Yin6,

Kristjan Haule6, Gabriel Kotliar6 & Pengcheng Dai1,2,3

High-temperature superconductivity in iron pnictides occurs when electrons and holes are

doped into their antiferromagnetic parent compounds. Since spin excitations may be

responsible for electron pairing and superconductivity, it is important to determine their

electron/hole-doping evolution and connection with superconductivity. Here we use

inelastic neutron scattering to show that while electron doping to the antiferromagnetic

BaFe2As2 parent compound modifies the low-energy spin excitations and their correlation

with superconductivity (o50 meV) without affecting the high-energy spin excitations

(4100 meV), hole-doping suppresses the high-energy spin excitations and shifts the

magnetic spectral weight to low-energies. In addition, our absolute spin susceptibility

measurements for the optimally hole-doped iron pnictide reveal that the change in magnetic

exchange energy below and above Tc can account for the superconducting condensation

energy. These results suggest that high-Tc superconductivity in iron pnictides is associated

with both the presence of high-energy spin excitations and a coupling between low-energy

spin excitations and itinerant electrons.

DOI: 10.1038/ncomms3874 OPEN

1 Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China. 2 Department ofPhysics and Astronomy, Rice University, Houston, Texas 77005, USA. 3 Department of Physics and Astronomy, The University of Tennessee, Knoxville,Tennessee 37996-1200, USA. 4 ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire OX11 0QX, UK. 5 Center for Nanophase MaterialsSciences and Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6494, USA. 6 Department ofPhysics, Rutgers University, Piscataway, New Jersey 08854, USA. * These authors contributed equally to this work. Correspondence and requests formaterials should be addressed to P.D. (email: [email protected]).

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In conventional Bardeen-Cooper-Schrieffer (BCS) supercon-ductors1, superconductivity occurs when electrons formcoherent Cooper pairs below the superconducting transition

temperature Tc. Although the kinetic energy of paired electronsincreases in the superconducting state relative to the normal state,the reduction in the ion lattice energy is sufficient to give thesuperconducting condensation energy (Ec¼ �N(0)D2/2 andDE2:oDe� 1=Nð0ÞV0 , where N(0) is the electron density of statesat zero temperature, :oD is the Debye energy, and V0 is thestrength electron-lattice coupling)1–3. For iron pnictidesuperconductors derived from electron or hole-doping of theirantiferromagnetic (AF) parent compounds4–9, the microscopicorigin for superconductivity is unclear. Although spin excitationsarising from quasiparticle excitations between the hole pocketsnear G and electron pockets at M in reciprocal space have beensuggested as the microscopic origin for superconductivity10,11,orbital fluctuations may also induce superconductivity in thesematerials12. Here we use inelastic neutron scattering (INS) tosystematically map out energy and wave vector dependence of thespin excitations in electron and hole-doped iron pnictides withdifferent superconducting transition temperatures. By comparingthe outcome with previous spin wave measurements on theundoped parent compound BaFe2As2 (ref. 13), we find thathigh-Tc superconductivity only occurs for iron pnictides withlow-energy (r25 meV or B6.5 kBTc) itinerant electron-spin excitation coupling and high-energy (4100 meV) spinexcitations. Since our absolute spin susceptibility measurementsfor optimally hole-doped iron pnictide reveal that the change inmagnetic exchange energy below and above Tc

14,15 can accountfor the superconducting condensation energy, we suggest that thepresence of both high-energy spin excitations giving rise to a largemagnetic exchange coupling J and low-energy spin excitationscoupled to the itinerant electrons are important for high-Tc

superconductivity in iron pnictides.For BCS superconductors, the superconducting condensation

energy Ec and Tc are controlled by the strength of the Debyeenergy :oD and electron-lattice coupling V0 (refs 1–3). Amaterial with large :oD and lattice exchange coupling is anecessary but not a sufficient condition to have high-Tc

superconductivity. On the other hand, a soft metal with small:oD (such as lead and mercury) will also not exhibitsuperconductivity with high-Tc. For unconventionalsuperconductors such as iron pnictides, the superconductingphase is derived from hole and electron doping from their AFparent compounds4–9. Although the static long-range AF order isgradually suppressed when electrons or holes are doped into theiron pnictide parent compound such as BaFe2As2 (refs 5–9),short-range spin excitations remain throughout thesuperconducting phase and are coupled directly with theoccurrence of superconductivity16–25. For spin excitations-mediated superconductors, the superconducting condensationenergy should be accounted for by the change in magneticexchange energy between the normal (N) and superconducting(S) phases at zero temperature. For an isotropic t-J model26,DEex(T)¼ 2J[/Siþ x � SiSN�/Siþ x � SiSS], where J is the nearestneighbour magnetic exchange coupling and /Siþ x � SiS is thedynamic spin susceptibility in absolute units at temperatureT14,15. Since the dominant magnetic exchange couplings areisotropic nearest neighbour exchanges for copper oxidesuperconductors27,28, the magnetic exchange energy DEex(T)can be directly estimated using the formula through carefullymeasuring of J and the dynamic spin susceptibility in absoluteunits between the normal and superconducting states29–31. Forheavy Fermion superconductor such as CeCu2Si2, one has tomodify the formula to include both the nearest neighbour andnext nearest neighbour magnetic exchange couplings appropriate

for the tetragonal unit cell of CeCu2Si2 to determine DEex(T)(ref. 32). In the case of iron pnictide superconductors5–9, theeffective magnetic exchange couplings in their parent compoundsare strongly anisotropic along the nearest neighbour ao and bo

axis directions of the orthorhombic structure (see inset inFig. 1a)13,33,34. Although the electron doping induced latticedistortions in iron pnictides35 may affect the effective magneticexchange couplings36, our INS experiments on optimallyelectron-doped BaFe1.9Ni0.1As2 indicate that the high-energyspin excitations, which determines the effective magnetic ex-change couplings13,33,34, are weakly electron doping-dependent24.Therefore, we can rewrite the relation between the magneticexchange coupling and the magnetic exchange energy as15

EexðTÞ ¼Xoi;j4

JijhSi � Sji¼3

pg2m2B

ZdQ2

ð2pÞ2Z

do

Xi

J1a½1þ nðo;TÞ�w00 ðQ;oÞcosðqxÞ(

þX

i

J1b½1þ nðo;TÞ�w00 ðQ;oÞcosðqyÞ

þX

i

J2½1þ nðo;TÞ�w00 ðQ;oÞ½cosðqx þ qyÞþ cosðqx � qyÞ�)

ð1Þ

Here the scattering function S(Q,E¼ :o) is related to theimaginary part of the dynamic susceptibility w

00(Q,o) via

S(Q,o)¼ [1þ n(o,T)]w00(Q,o), where [1þ n(o,T)] is the Bose

population factor, Q the wave vector, and E¼ :o the excitationenergy. J1a is the effective magnetic coupling strength betweentwo nearest sites along the ao direction, while J1b is that along thebo direction and J2 is the coupling between the next nearestneighbour sites (see inset in Fig. 1a)13.

To determine how high-Tc superconductivity in iron pnictidesis associated with spin excitations, we consider the phase diagramof electron and hole-doped iron pnictide BaFe2As2 (Fig. 1a)9. Inthe undoped state, BaFe2As2 forms a metallic low-temperatureorthorhombic phase with collinear AF structure as shown in theinset of Fig. 1a. INS measurements have mapped out spin wavesthroughout the Brillouin zone and determined the effectivemagnetic exchange couplings13. Upon doping electrons toBaFe2As2 by partially replacing Fe with Ni to inducesuperconductivity in BaFe2� xNixAs2 with maximum TcE20 Kat xe¼ 0.1 (ref. 37), the low-energy (o80 meV) spin waves in theparent compounds are broadened and form a neutron spinresonance coupled to superconductivity20–23, while high-energyspin excitations are weakly affected24. With further electrondoping to xeZ0.25, superconductivity is suppressed and thesystem becomes a paramagnetic metal (Fig. 1a)37. For hole-dopedBa1� xKxFe2As2 (ref. 38), superconductivity with maximumTc¼ 38.5 K appears at xhE0.33 (ref. 5) and pure KFe2As2 atxh¼ 1 is a Tc¼ 3.1 K superconductor6. In order to determine howspin excitations throughout the Brillouin zone are correlated withsuperconductivity in iron pnictides, we study optimally hole-doped Ba0.67K0.33Fe2As2 (Tc¼ 38.5 K, Fig. 1c), pure KFe2As2

(Tc¼ 3 K, Fig. 1b), and nonsuperconducting electron-overdopedBaFe1.7Ni0.3As2 (Fig. 1d). If spin excitations are responsible formediating electron pairing and superconductivity, the change inmagnetic exchange energy between the normal andsuperconducting state should be large enough to account forthe superconducting condensation energy15.

From density functional theory (DFT) calculations, onefinds that Fermi surfaces for the undoped parent compoundBaFe2As2 consist of hole-like pockets near the Brillouin zonecentre and electron pockets near the zone corner (Fig. 2a)10.

ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms3874

2 NATURE COMMUNICATIONS | 4:2874 | DOI: 10.1038/ncomms3874 | www.nature.com/naturecommunications



Figure 2a–d shows the evolution of Fermi surfaces as a functionof electron- and hole-doping obtained from the tight-bindingmodel of Graser et al.39 When electrons are doped into the parentcompounds, the hole Fermi surfaces decrease in size while the

electron pocket sizes increase (Fig. 2b)40. As a consequence,quasiparticle excitations between the hole and electron Fermisurfaces form transversely elongated spin excitations that increasewith increasing electron doping23–25. For electron-overdoped

R (

mΩ

cm

)

0.05

0.1

0.15

0.2

0 100 200 300T (K)

0

[1, K] (r.l.u.)

1.0 0.5 0.5 1.0

4��

10

20

30

40

�”(�

) (�

B2 e

V–1

f.u.

–1)

0

0 100 200 300

E (meV)

0 20 40 600 2 6T (K)T (K)

0 11.0 0.5 1.25 1.5

[1, K]

0

200

100

10.6 0.8 1.2 1.4

[H, 0] (r.l.u.)

0

40

20

E (

meV

)

�”(ω

)

50

Doping concentration (x)

0 0.1 0.30.20.250.50.751.0

40

80

120

160

T (

K)

BaFe2-xNixAs2Ba1-xKxFe2As2

SC

AFM

PM

AFM

PM

a

SC

(1,0)

IC-SF

H

KC-SF

H

K

(1,0)

Fe2+ Asbo

ao

IC-AFM

BaFe1.7Ni0.3As2Ba0.67K0.33Fe2As2

xe=0.3x=0

–0.8

–0.4

0KFe2As2

b c d

gfe

xe=0.1, 5 K

xe=0.3, 5 K

xe=0.3

xh=0.33xh=1.0

xh=0.33, 9 K

xh=0.33, 45 K

h

xh=0.33

x=0

0

5

10

20 40 60E (meV)

x=0xh=1

xh=1

T=5 K

J2

J1a

J1b

4

Tc=3.1 K

Tc

Tc=38.5 KTc

[H, 0] (r.l.u.)

Figure 1 | Summary of transport and neutron scattering results. (a) The electronic phase diagram of electron and hole-doped BaFe2As2 (ref. 9). The right

inset shows crystal and AF spin structures of BaFe2As2 with marked the nearest (J1a, J1b) and next nearest neighbor (J2) magnetic exchange couplings.

The left insets show the evolution of low-energy spin excitations in Ba1� xKxFe2As2. (b,c) Temperature dependence of magnetic susceptibility for our

KFe2As2 and Ba0.67K0.33Fe2As2. (d) Temperature dependence of the resistivity for BaFe1.7Ni0.3As2. (e–g) The filled circles are spin excitation dispersions of

KFe2As2 at 5 K, Ba0.67K0.33Fe2As2 at 9 K, and BaFe1.7Ni0.3As2 at 5 K, respectively. The shaded areas indicate vanishing spin excitations and the solid lines

show spin wave dispersions of BaFe2As2 (ref. 13). (h) Energy dependence of w00(o) for BaFe1.9Ni0.1As2 (dashed line), BaFe1.7Ni0.3As2 (green solid circles),

Ba0.67K0.33Fe2As2 below (solid red circles and solid red line) and above (open purple circles and solid lines) Tc. The inset shows Energy dependence of

w00(o) for KFe2As2. The vertical error bars indicate the statistical errors of one standard deviation. The horizontal error bars in (h) indicate the energy

integration range.

NATURE COMMUNICATIONS | DOI: 10.1038/ncomms3874 ARTICLE




iron pnictides, the hole pockets sunk below the Fermi surface(Fig. 2c)40. The absence of interband transition between the holeand electron Fermi surfaces is expected to result in a completesuppression of the low-energy spin excitations at the AFordering wave vector. This is indeed confirmed by nuclearmagnetic resonance experiments on electron overdopedBa(Fe1� xCox)2As2 (ref. 41). For optimally hole-doped ironpnictide Ba0.67K0.33Fe2As2 (inset in Fig. 1a), DFT theory basedon sign reversed quasiparticle excitations between hole andelectron pockets (Fig. 2d) predicts correctly the longitudinallyelongated spin excitations from QAF¼ (1,0)23,18. In addition, INSwork on powder16,17 and single crystals18 of hole-dopedBa1� xKxFe2As2 reveal that the low-energy spin excitations aredominated by a resonance coupled to superconductivity. For pureKFe2As2 (xh¼ 1), low-energy (o14 meV) spin excitationsbecome longitudinally incommensurate from QAF¼ (1,0) (insetin Fig. 1a)19. These results, as well as the work on electron-dopediron pnictides23–25, have shown that the low-energy spinexcitations in iron-based superconductors can be accountedfor by itinerant electrons on the hole and electron-nested Fermisurfaces9.

Here we use INS to show that the effect of hole-doping toBaFe2As2 is to suppress high-energy spin excitations and transferthe spectral weight to low-energies that couple to the appearanceof superconductivity (Fig. 1h). The overall spin excitationsspectrum in optimally hole-doped superconducting Ba0.67

K0.33Fe2As2 is qualitatively consistent with theoretical methodsbased on DFT and dynamic mean filed theory (DMFT)42.By using the INS measured magnetic exchange couplingsand spin susceptibility in absolute units, we calculate thesuperconductivity-induced lowering of magnetic exchangeenergy and find it to be about seven times larger than thesuperconducting condensation energy determined from specificheat measurements for Ba0.67K0.33Fe2As2 (ref. 43). These results

are consistent with spin excitations-mediated electron pairingmechanism15. For the nonsuperconducting electron-overdopedBaFe1.7Ni0.3As2, we find that while the effective magneticexchange couplings are similar to that of optimally electron-doped BaFe1.9Ni0.1As2 (Fig. 1g)24, the low-energy spin excitations(o50 meV) associated with the hole and electron pocket Fermisurface nesting disappear (Fig. 2c), thus revealing the importanceof Fermi surface nesting and itinerant electron-spin excitationcoupling to the occurrence of superconductivity (Fig. 1h). Finally,for heavily hole-doped KFe2As2 with low-Tc superconductivity(Fig. 1b), there are only incommensurate spin excitations belowB25 meV possibly due to the mismatched electron-hole Fermisurfaces19,44 and the correlated high-energy spin excitationsprevalent in electron-doped and optimally hole-doped ironpnictides are strongly suppressed (Fig. 1e), indicating adramatic softening of effective magnetic exchange coupling(inset Fig. 1h). Therefore, high-Tc superconductivity is likelyassociated with two ingredients: a large effective magneticexchange coupling15, much like the large Debye energy forhigh-Tc BCS superconductors, and a strong itinerant electrons-spin excitations coupling from the Fermi surface nesting10,similar to electron-phonon coupling in BCS superconductors.

ResultsElectron and hole-doping evolution of spin excitations. Tosubstantiate the key conclusions of Fig. 1, we present the two-dimensional (2D) constant-energy images of spin excitations inthe (H,K) plane at different energies for KFe2As2 (Fig. 3a–c),Ba0.67K0.33Fe2As2 (Fig. 3d–f), and BaFe1.7Ni0.3As2 (Fig. 3g–i)above Tc. In previous INS work on KFe2As2, longitudinalincommensurate spin excitations were found by triple axisspectrometer measurements for energies from 3 to 14 meV in thenormal state19. While we confirmed the earlier work using time-of-flight INS for energies below E¼ 15±1 meV (Fig. 3a,b), ournew data collected at higher excitation energies reveal thatincommensurate spin excitations converge into a broad spinexcitation near E¼ 20 meV and disappear for energies above25 meV (Fig. 3c; Supplementary Fig. S1). For Ba0.67K0.33Fe2As2,spin excitations at E¼ 5±1 meV are longitudinally elongatedfrom QAF as expected from the DFT calculations (Fig. 3d)18,23.At the resonance energy (E¼ 15±1 meV)16, spin excitations areisotropic above Tc (Fig. 3e). On increasing energy further toE¼ 50±10 meV, spin excitations change to transverselyelongated from QAF similar to spin excitations in optimallyelectron-doped superconductor BaFe1.9Ni0.1As (Fig. 3f)24.Figure 3g–i summarizes similar 2D constant-energy images ofspin excitations for nonsuperconducting BaFe1.7Ni0.3As. AtE¼ 9±3 (Fig. 3g) and 30±10 meV (Fig. 3h), there are nocorrelated spin excitations near the QAF. Upon increasing energy toE¼ 59±10 meV (Fig. 3i), we see clear spin excitations transverselyelongated from QAF (Fig. 3i; Supplementary Fig. S2). To furtherillustrate the presence of a large spin gap in BaFe1.7Ni0.3As, wecompare spin waves in BaFe2As2

13 and paramagnetic spinexcitations in BaFe1.7Ni0.3As. Figure 4a,b shows the backgroundsubtracted spin wave scattering of BaFe2As2 for the Ei¼ 250,450 meV data, respectively, projected in the wave vector(Q¼ [1,K]) and energy space at 7 K13. Sharp spin waves are seento stem from the AF ordering wave vector QAF¼ (1,0) above theB15 meV spin gap45. Figure 4c,d shows identical projections forspin excitations of BaFe1.7Ni0.3As at 5 K. A large spin gap ofB50 meV is clearly seen in the data near QAF¼ (1,0). A detailedcomparison of spin excitations in BaFe2� xNixAs2 with xe¼ 0, 0.1,0.3 is made in Supplementary Figs S3 and S4.

Figure 5a–d shows 2D images of spin excitations inBaFe1.7Ni0.3As2 at E¼ 70±10, 112±10, 157±10, and

0H (r.l.u.)

0

1

K (

r.l.u

.)

dxz dyz dxy

γ

β1

α1

α2

β2

1

x=0

10H (r.l.u.)

0

1

K (

r.l.u

.)

xe=0.3

0H (r.l.u.)

0

1

K (

r.l.u

.)

1

xe=0.1

10H (r.l.u.)

0

1

K (

r.l.u

.)

xh=0.33

Figure 2 | Schematics of Fermi surface evolution as a function of

Ni-doping for BaFe2� xNixAs2 and for Ba0.67K0.33Fe2As2. (a–c) Evolution

of Fermi surfaces with Ni-dopings of xe¼0,0.1,0.3. The dxz, dyz, and dxy

orbitals for different Fermi surfaces are coloured as red, green and blue,

respectively. (d) Fermi surfaces for Ba0.67K0.33Fe2As2.





214±10 meV, respectively. Figure 5e–h shows wave vectordependence of spin excitations at energies E¼ 70±10, 115±10,155±10 and 195±10 meV, respectively, for Ba0.67K0.33Fe2As2.

Similar to spin waves in BaFe2As2 (ref. 13), spin excitationsin BaFe1.7Ni0.3As2 and Ba0.67K0.33Fe2As2 split along theK-direction for energies above 80 meV and form rings aroundQ¼ (±1,±1) positions near the zone boundary, albeit at slightlydifferent energies. Comparing spin excitations in Fig. 5a–d forBaFe1.7Ni0.3As2 with those in Fig. 5e–h for Ba0.67K0.33Fe2As2 inabsolute units, we see that spin excitations in BaFe1.7Ni0.3As2

extend to slightly higher energies and have larger intensity above100 meV.

As discussed in the spin wave measurements of BaFe2As2

(ref. 13), the magnon band top energy at Q¼ (1,1) governs theeffective magnetic exchange couplings J (J1a, J1b, and J2). Toestimate the change of J for hole-doped Ba0.67K0.33Fe2As2, wecalculate the energy cut at Q¼ (1,1) by exploring the HeisenbergHamiltonian of the parent compound. It turns out that J1a, J1b,and J2 have comparable effect on the band top. On the basis of thedispersion of Ba0.67K0.33Fe2As2, the effective magnetic exchange Jis found to be about 10% smaller for Ba0.67K0.33Fe2As2 comparedwith that of BaFe2As2 (Fig. 6). For comparison, if we assume theband top for KFe2As2 is around E¼ 25 meV, the effectivemagnetic exchange should be about 90% smaller for KFe2As2.Of course, we know this is not an accurate estimation since spinexcitations in KFe2As2 are incommensurate and have an inversedispersion. In any case, given the zone boundary energy ofEE25 meV (Supplementary Fig. S1), the effective magneticexchange couplings in KFe2As2 must be much smaller than thatof BaFe2As2.

H (r.l.u.)

0

1

–1K

(r.

l.u.)

K (

r.l.u

.)

0

1

–1

H (r.l.u.) H (r.l.u.)

–2

3

1 20

K (

r.l.u

.)

1 20

0

–11 20

1

–2

7

–2

7

–2

3

–0.5

2.5

–2

5

–0.3

0.8

–1

3

–0.3

1.1

KFe2As2 Bs0.67K0.33Fe2AS2 BaFe1.7Ni0.3As2

8±3 meV 5±1 meV 9±3 meV

13±3 meV 15±1 meV 30±10 meV

59±10 meV50±2 meV53±8 meV

+

+

+

+

+

Figure 3 | Constant-energy slices through magnetic excitations of iron pnictides at different energies. The colour bars represent the vanadium

normalized absolute spin excitation intensity in the units of mbarn sr� 1 meV� 1 f.u.� 1. 2D images of spin excitations at 5 K for KFe2As2 (a) E¼ 8±3 meV

obtained with Ei¼ 20 meV. The right side incommensurate peak is obscured by background scattering. (b) 13±3 meV with Ei¼ 35 meV, (c) 53±10 meV

with Ei¼ 80 meV. For Ba0.67K0.33Fe2As2 at T¼45 K, images of spin excitations at (d) E¼ 5±1 meV obtained with Ei¼ 20 meV, (e) 15±1 meV with

Ei¼ 35 meV, and (f) 50±2 meV obtained with Ei¼80 meV. The dashed box in (d) indicates the AF zone boundaries for a single FeAs layer and the black

dashed lines mark the orientations of spin excitations at different energies. Images of spin excitations for BaFe1.7Ni0.3As2 at T¼ 5 K and (g) E¼ 9±3 meV

obtained with Ei¼ 80 meV, (h) 30±10 meV with Ei¼450 meV, and (i) 59±10 meV with Ei¼ 250 meV. The white crosses indicate the position of QAF.

0

100

150

0

1.2

50

0–1–2 210

100

150

0

5

x=0, Ei=250 meV

x=0, Ei=450 meV

xe=0.3, Ei=250 meV

xe=0.3, Ei=450 meV

E (

meV

)

50

0–1–2 21

0

200

300

0

2

100

0–1–2 210

200

300

0

2

E (

meV

)

100

0–1–2 21

[1, K ] (r.l.u.) [1, K ] (r.l.u.)

Figure 4 | The dispersion of spin excitations for BaFe2� xNixAs2 along the

[1,K] direction. (a,b) The dispersion cuts of BaFe2As2 with Ei¼ 250 meV

and Ei¼450 meV along [1,K] direction. The data are from MAPS13.

(c,d) Identical dispersion cuts of BaFe1.7Ni0.3As2 (xe¼0.3) at MAPS.





Theoretical calculations of spin excitations. To understand thewave vector dependence of spin excitations in hole-dopedBa0.67K0.33Fe2As2, we have carried out the random phaseapproximation (RPA) calculation of the dynamic susceptibility ina pure itinerant electron picture using the method describedbefore25. Figure 5i,j shows RPA calculations of spin excitations atE¼ 70 and 155 meV, respectively, for Ba0.67K0.33Fe2As2 assumingthat hole doping induces a rigid band shift25. While a pure RPAtype itinerant model can explain longitudinally elongated spinexcitations at low-energies18, it clearly fails to describe thetransversely elongated spin excitations in hole-doped iron

pinctides at high energies (Fig. 5e,g). For comparison with theRPA calculation, we also used a combined DFT and DMFTapproach24,42 to calculate the imaginary part of the dynamicsusceptibility w

00(Q,o) in the paramagnetic state. Figure 5k,i

shows calculated spin excitations at E¼ 70 and 155 meV,respectively. Although the model still does not agree in detailwith the data in Fig. 5e,g, it captures the trend of spectral weighttransfer away from QAF¼ (1,0) on increasing energy and forminga pocket centred at Q¼ (1,1).

Dispersions of spin excitations and local dynamic suscept-ibility. By carrying out cuts through the 2D images similar toFigs 3d–f and 5e–h along the [1,K] and [H,0] directions

2

–2

70±10meV 112±10meV 157±10meV 214±10meV

–0.3

1.0

–0.3 –0.3 –0.2

0.7 0.7 0.4

BaF

e 1.7N

i 0.3A

s 2

K (

r.l.u

.)

2

–2

70±10meV 115±10meV 155±10meV 195±10meV

–0.3

1.0

–0.3

0.7

–0.3

0.7

–0.2

0.4

Ba 0.

67K

0.33

Fe 2A

s 2

K (

r.l.u

.)

0 2–2H (r.l.u.)

2–2 2–2

2

–20 2–2

70 meV 155 meV 70 meV 155 meV

H (r.l.u.) H (r.l.u.) H (r.l.u.)

Min

Max

Ba 0.

67K

0.33

Fe 2A

s 2

K (

r.l.u

.)

DMFTRPA RPA DMFT

0

0

0

0 0

S(Q

,�)

(mbr

sr–1

meV

–1f.u

.–1)

Figure 5 | Constant-energy images of spin excitations of iron pnictides and its comparison with RPA/DMFT calculations. Spin excitations of

BaFe1.7Ni0.3As2 in the 2D [H,K ] plane at energy transfers of (a) E¼ 70±10 meV obtained with Ei¼ 250 meV; (b) 112±10 meV Ei¼ 250 meV;

(c) 157±10 meV and (d) 214±10 meV with Ei¼450 meV. All obtained at 5 K. A flat backgrounds have been subtracted from the images. Spin excitations

of Ba0.67K0.33Fe2As2 at energy transfers of (e) E¼ 70±10 meV obtained with Ei¼ 170 meV; (f) 115±10 meV; (g) 155±10 meV; (h) 195±10 meV obtained

with Ei¼450 meV, all at 9 K. Wave vector dependent backgrounds have been subtracted from the images. RPA calculations25 of spin excitations for

Ba0.67K0.33Fe2As2 at (i) E¼ 70 meV and (j) E¼ 155 meV. DMFT calculations24,42 for Ba0.67K0.33Fe2As2 at (k) E¼ 70 meV and (l) E¼ 155 meV.

J

2.0

1.5 0.9 J0.125 J

Ba0.67K0.33Fe2As2

KFe2As2 BaFe2As2

1.0

0.5

0.0

0 25 50 100 200

Inte

nsity

(ar

b. u

nits

)

E (meV)

Figure 6 | The effect of magnetic exchange couplings J (J1a, J1b and J2)

on the band top of spin excitations. The black line is energy cut at

(0.8oHo1.2, 0.8oKo1.2) r.l.u for BaFe2As2 in the Heisenberg spin wave

model13. The red line is for Ba0.67K0.33Fe2As2 with 10 % soften band

top. The blue line is a similar estimation for KFe2As2 assuming zone

boundary is around E¼ 25 meV.

BaFe2As2 DMFT

Ba0.67K0.33Fe2As2

BaFe1.9Ni0.1As2

RPA

KFe2As2

χ′′(�

) (�

B2

eV–1

f.u.

–1)

E (meV)0 100 200 300

20

10

0

30

40

Figure 7 | RPA and LDAþDMFT calculated local susceptibility for

different iron pnictides. RPA and LDAþDMFT calculations of w00(o) in

absolute units for KFe2As2 and Ba0.67K0.33Fe2As2 comparing with earlier

results for BaFe2As2 and BaFe1.9Ni0.1As224.





(Supplementary Figs S5 and S6), we establish the spin excitationdispersion along the two high symmetry directions forBa0.67K0.33Fe2As2 and compare with the dispersion of BaFe2As2

(Fig. 1f )13. In contrast to the dispersion of electron-dopedBaFe1.9Ni0.1As2 (ref. 24), we find clear softening of the zoneboundary spin excitations in hole-doped Ba0.67K0.33Fe2As2 fromspin waves in BaFe2As2 (ref. 13). We estimate that the effectivemagnetic exchange coupling in Ba0.67K0.33Fe2As2 is reduced byabout 10% from that of BaFe2As2 (Fig. 6). Similarly, Fig. 1g showsthe dispersion curve of BaFe1.7Ni0.3As2 along the [1,K] directionplotted together with that of BaFe2As2 (ref. 13). For energiesbelow B50 meV, spin excitations are completely gapped marked

in the dashed area probably due to the missing hole-electronFermi pocket quasiparticle excitations40. On the basis of the 2Dspin excitation images similar to Fig. 3a–c; we plot in Fig. 1e thedispersion of incommensurate spin excitations in KFe2As2. Theincommensurability of spin excitations is weakly energydependent below E¼ 12 meV but becomes smaller withincreasing energy above 12 meV. Correlated spin excitations forenergies above 25 meV are suppressed as shown in the shadedarea in Fig. 1e.

To quantitatively determine the effect of electron and holedoping on the overall spin excitations spectra, we calculate thelocal dynamic susceptibility per formula unit (f.u.) in absolute

100%

–50%

E = 15±1 meV

K (

r.l.u

)K

(r.l

.u)

H (r.l.u) H (r.l.u)

E (meV)T (K)

Tc = 38.5 K

T (K) T (K)

Ec

(J m

ol–1

)

E (

meV

)FWHM

(r.l

.u)

ΔS (� B

2 eV

–1 f.

u.–1

)

38 K

45 K40 K

25 K

0.25

0.00

–0.25

0.25

–0.25

0.25

0.30

0.35

0.40

7

0

14

21

28

55

0 0

10

15

20

0.00

0.5

0 5 15 25 35–3

3

6

0 χ′′(a

rb. u

nits

)

10 10

10

15

20 2030 3040 50

0 10 20 30 40 50 0 10 20 30 40 50

1.0 1.5 0.5 1.0 1.5

9 K

30 K

15 K

20 K

25 K

33 K

35 K

38 K

40 K

ERΔα1+Δβ

ΔS

EC

Figure 8 | Properties of the resonance across Tc¼38.5 K for Ba0.67K0.33Fe2As2. Constant-energy (E¼ 15±1 meV) images of spin excitations at

(a) T¼ 25, (b) 38, (c) 40, and (d) 45 K obtained with Ei¼ 35 meV. In order to make fair comparison of the scattering line shape at different temperatures,

the peak intensity at each temperature is normalized to 1. The pink and green arrows in (a) mark wave vector cut directions across the resonance.

The integration ranges are �0.2rKr0.2 along the [H,0] direction and 0.8rHr1.2 along the [1,K] direction. The full-width-at-half-maximum (FWHM) of

spin excitations are marked as dashed lines. (e) The FWHM of the resonance along the [H,0] and [1,K] directions as a function of temperature

across Tc. (f) Energy dependence of the resonance obtained by subtracting the low-temperature data from the 45 K data, and correcting for the Bose

population factor. (g) The black diamonds show temperature dependence of the sum of hole and electron pocket electronic gaps obtained from Angle

Resolved Photoemission experiments for Ba0.67K0.33Fe2As2 (ref. 40). The red solid circles show temperature dependence of the resonance.

(h) Temperature dependence of the superconducting condensation energy from heat capacity measurements43 and the intensity of the resonance

integrated from 14–16 meV. The error bars indicate the statistical errors of one s.d.





units, defined as w00(o)¼

Rw00(q,o)dq/

Rdq (ref. 24), where

w00ðq;oÞ¼ð1=3Þtrðw00abðq;oÞÞ, at different energies for Ba0.67

K0.33Fe2As2, BaFe1.7Ni0.3As2, and KFe2As2. Figure 1h shows theoutcome together with previous data on optimally electron-dopedsuperconductor BaFe1.9Ni0.1As2 (ref. 24). While electron dopingup to BaFe1.7Ni0.3As2 does not change much the spectral weightof high-energy spin excitations from that of BaFe1.9Ni0.1As2, hole-doping dramatically suppresses the high-energy spin excitationsand shift the spectral weight to lower energies (Fig. 1h). Forheavily hole-doped KFe2As2, spin excitations are mostly confinedto energies below about E¼ 25 meV (inset in Fig. 1h).

The solid green, red, black, and blue lines in Fig. 7 showcalculated local susceptibility in absolute units based on acombined DFT and DMFT approach for KFe2As2, Ba0.67K0.33-

Fe2As2, BaFe2As2, and BaFe1.9Ni0.1As224, respectively. This

theoretical method predicts that electron doping to BaFe2As2

does not affect the spin susceptibility at high energy(E4150 meV), while spin excitations in the hole-dopedcompound beyond 100 meV are suppressed by shifting thespectral weight to lower energies. This is in qualitative agreementwith our absolute intensity measurements (Fig. 1h). Thereduction of the high-energy spin spectral weight and itstransfer to low energy with hole doping, but not with electrondoping, is not naturally explained by the band theory (Fig. 7) andrequires models that incorporate both the itinerant quasiparticlesand the local moment physics9,42. The hole doping makes theelectronic state more correlated, as local moment formation isstrongest in the half-filled d5 shell, and mass enhancement largerthereby reducing the electronic energy scale in the problem. Thedashed lines in Fig. 7 show the results of calculated localsusceptibility using RPA, which clearly fails to describe theelectron- and hole-doping dependence of the local susceptibility.

Estimation of the superconductivity-induced magneticexchange energy. Finally, to determine how low-energy spinexcitations are coupled to superconductivity in Ba0.67K0.33Fe2As2,we carried out a detailed temperature-dependent study of spinexcitation at E¼ 15±1 meV. Comparing with strongly c axismodulated low-energy (Eo7 meV) spin excitations18, spinexcitations at the resonance energy are essentially 2D withoutmuch c axis modulations. In previous work18, we have shown thatspin excitations near the neutron spin resonance are longi-tudinally elongated and change dramatically in intensity acrossTc. However, these measurements are obtained in arbitrary unitsand therefore cannot be used to determine the magnetic exchangeenergy. Figure 8a–d shows the 2D mapping of the resonance atT¼ 25, 38, 40, and 45 K, respectively. While the resonance revealsa clear oval shape at temperatures below Tc consistent withearlier work (Fig. 8a,b)18, it changes into an isotropic circularshape abruptly at Tc (Fig. 8c,d) as shown by the dashed linesrepresenting full-width-at-half-maximum of the excitations(Supplementary Fig. S7). Temperature dependence of theresonance width along the [H,0] and [1,K] directions in Fig. 8ereveals that the isotropic to anisotropic transition in momentumspace occurs at Tc. Figure 8f shows temperature dependence ofthe resonance from 9–40 K, which vanishes at Tc. Figure 8g plotstemperature dependence of the mode energy together with thesum of the superconducting gaps from the hole and electronpockets40. Figure 8h compares temperature dependence of thesuperconducting condensation energy43 with superconductivity-induced intensity gain of the resonance. By calculating spinexcitations induced changes in magnetic exchange energy usingequation (1) (see Methods and Supplementary Fig. S8)15, we findthat the difference of magnetic exchange interaction energybetween the superconducting and normal state is approximately

seven times larger than the superconducting condensationenergy43, thus indicating that AF spin excitations can be themajor driving force for superconductivity in Ba0.67K0.33Fe2As2.

DiscussionOne way to quantitatively estimate the impact of hole/electrondoping and superconductivity to spin waves of BaFe2As2 is todetermine the energy dependence of the local moment and totalfluctuating moments /m2S (ref. 24). From Fig. 1h, we see thathole-doping suppresses high-energy spin waves of BaFe2As2 andpushes the spectral weight to resonance at lower energies. Thetotal fluctuating moment of Ba0.67K0.33Fe2As2 below 300 meV is/m2S¼ 1.7±0.3 per Fe, somewhat smaller than 3:2 � 0:16 m2

Bper Fe for BaFe2As2 and BaFe1.9Ni0.1As2 (ref. 24). For com-parison, BaFe1.7Ni0.3As2 and KFe2As2 have /m2S¼ 2.74±0.11and 0:1 � 0:02 m2

B per Fe, respectively. Therefore, the totalmagnetic spectral weights for different iron pnictides have nodirect correlation with their superconducting Tcs. Table 1summarizes the comparison of effective magnetic exchangecouplings, total fluctuating moments, and spin excitation bandwidths for BaFe2� xNixAs2 with xe¼ 0,0.1,0.3 and Ba1� xKxFe2As2

with xh¼ 0.33, 1.From Fig. 1h, we also see that the spectral weight of the

resonance and low-energy (o100 meV) magnetic scattering inBa0.67K0.33Fe2As2 is much larger than that of electron-dopedBaFe1.9Ni0.1As2. This is consistent with a large superconductingcondensation energy in Ba0.67K0.33Fe2As2 since its effectivemagnetic exchange coupling J is only B10% smaller than thatof BaFe1.9Ni0.1As2 (Fig. 1h)43,46. For electron-overdoped non-superconducting BaFe1.7Ni0.3As2, the lack of superconductivity iscorrelated with the absence of low-energy spin excitationscoupled to the hole and electron Fermi surface nesting eventhough the effective magnetic exchange couplings remainlarge40,41. This means that by eliminating [/Siþ x � SiSN�/Siþ x � SiSS], there is no magnetic driven superconductingcondensation energy, and thus no superconductivity. On theother hand, although the suppression of correlated high-energyspin excitations in KFe2As2 can dramatically reduce the effectivemagnetic exchange coupling in KFe2As2 (Figs 1e and 6), onecan still have superconductivity with reduced Tc. If spinexcitations are a common thread of the electron pairinginteractions for unconventional superconductors15, our resultsreveal that the large effective magnetic exchange couplings anditinerant electron-spin excitation interactions may both beimportant ingredients to achieve high-Tc superconductivity,much like the large Debye energy and the strength of electron-lattice coupling are necessary for high-Tc BCS superconductors.Therefore, our data indicate a possible correlation between theoverall magnetic excitation band width, the presence oflow-energy spin excitations, and the scale of Tc. This suggeststhat both high-energy spin excitations and low-energy spin

Table 1 | Summary of properties of various iron pnictides.

Compounds SJ1a/SJ1b

(meV)SJ2a/SJ2b

(meV)hM2iðl2

BÞ/Fe Band width(meV)

BaFe2As2 59.2/�9.2 13.6/13.6 3.6 15–200BaFe1.9Ni0.1As2 59.2/�9.2 13.6/13.6 3.2±0.2 0–200BaFe1.7Ni0.3As2 59.2/�9.2 13.6/13.6 2.7±0.1 50–200Ba0.67K0.33Fe2As2 53.3/�8.3 12.2/12.2 1.7±0.3 0–180KFe2As2 5.9/�0.9 1.4/1.4 0.1±0.02 0–25

The table shows a comparison of effective exchange couplings, total fluctuating moments andspin excitation band widths of BaFe2� xNixAs2 xe¼0,0.1,0.3 and Ba1� xKxFe2As2 xh¼0.33,1.





excitation itinerant electron coupling are important for high-Tc

superconductivity.

MethodsSample preparation. Single crystals of Ba0.67K0.33Fe2As2, KFe2As2, and BaFe1.7

Ni0.3As2 are grown using the flux method18,25. The actual crystal compositionswere determined using the inductively coupled plasma analysis. We coaligned 19 gof single crystals of Ba0.67K0.33Fe2As2 (with in-plane and out-of-plane mosaic of4�), 3 g of KFe2As2 (with in-plane and out-of-plane mosaic of B7.5�), and 40 g ofBaFe1.7Ni0.3As2 (with in-plane and out-of-plane mosaic of B3�).

Neutron scattering experiments. Our INS experiments were carried out on theMERLIN and MAPS time-of-flight chopper spectrometers at the Rutherford-Appleton Laboratory, UK13,24. Various incident beam energies were used asspecified, and mostly with Ei parallel to the c axis. To facilitate easy comparisonwith spin waves in BaFe2As2 (ref. 13), we defined the wave vector Q at (qx, qy, qz) as(H,K,L)¼ (qxao/2p, qybo/2p, qzc/2p) reciprocal lattice units (rlu) using theorthorhombic unit cell, where aoEbo¼ 5.57 Å, and c¼ 13.135 Å for Ba0.67K0.33

Fe2As2, aoEbo¼ 5.43 Å, and c¼ 13.8 Å for KFe2As2, and ao¼ bo¼ 5.6 Å, andc¼ 12.96 Å for BaFe1.7Ni0.3As2. The data are normalized to absolute units using avanadium standard with 20% errors24 and confirmed by acoustic phononnormalization (see Supplementary Note 1). Supplementary Discussion providesadditional data analysis on electron-doped iron pnictides, focusing on thecomparison of electron overdoped nonsuperconducting BaFe1.3Ni0.3As2 withoptimally electron-doped superconductor BaFe1.9Ni0.1As2 and AF BaFe2As2.

DFTþDMFT calculations. Our theoretical DFTþDMFT method for computingthe magnetic excitation spectrum employs the ab initio full potential imple-mentation of the method, as detailed in ref. 47. The DFT part is based on the codeof Wien2k48. The DMFT method requires solution of the generalized quantumimpurity problem, which is here solved by the numerically exact continuous-timequantum Monte Carlo method49,50. The Coulomb interaction matrix for electronson iron atom was determined by the self-consistent GW method in Kutepovet al.51, giving U¼ 5 eV and J¼ 0.8 eV for the local basis functions within the allelectron approach employed in our DFTþDMFT method. The dynamicalmagnetic susceptibility w

00(Q,E) is computed from the ab initio perspective by

solving the Bethe-Salpeter equation, which involves the fully interacting oneparticle Greens function computed by DFTþDMFT, and the two-particle vertex,also computed within the same method (for details see Park et al.42). We computedthe two-particle irreducible vertex functions of the DMFT impurity model, whichcoincides with the local two-particle irreducible vertex within the DFTþDMFTmethod. The latter is assumed to be local in the same basis in which the DMFTself-energy is local, here implemented by projection to the muffin-tin sphere.

Calculation of magnetic exchange energy and superconducting condensationenergy for Ba0.67K0.33Fe2As2. In a neutron scattering experiment, we measurescattering function S(Q,E¼ :o) which is related to the imaginary part of thedynamic susceptibility via S(Q,o)¼ [1þ n(o,T)]w

00(Q,o), where n(o,T) is the Bose

population factor. The magnetic exchange coupling and the imaginary part of spinsusceptibility are related via the formula15:

hSi � Sji¼3

pg2m2B

ZdQ2

ð2pÞ2Z

do½1þ nðo;TÞ�w00 ðQ;oÞcos½Q � ði� jÞ�; ð2Þ

where g¼ 2 is the Lande g-factor. Hence, we are able to obtain the change inmagnetic exchange energy between the superconducting and normal states by theexperimental data of w

00(Q,o) in both states using equation (1). Strictly speaking,

we want to estimate the zero temperature difference of the magnetic exchangeenergy between the normal and the superconducting states, and use the outcome tocompare with the superconducting condensation energy15. Unfortunately, we donot have direct information on the normal state w

00(Q,o) at zero temperature.

Nevertheless, since our neutron scattering measurements at low-energies showedthat the w

00(Q,o) are very similar below and above Tc near the AF wave vector

QAF¼ (1,0,1) and only a very shallow spin gap at Q¼ (1,0,0) (see Fig. 1f,h in Zhanget al.18), we assume that there are negligible changes in w

00(Q,o) above and below Tc

at zero temperature for energies below 5 meV. For spin excitation energies above6 meV, the Bose population factors between 7 and 45 K are negligibly small. Inprevious work on optimally doped YBa2Cu3O6.95 superconductor, we haveassumed that spin excitations in the normal state at zero temperature are negligiblysmall and thus do not contribute to the exchange energy30.

The directly measured quantity is the scattering differential cross section

d2sdOdE

ki

kf¼ 2ðgreÞ2

pg2m2Bj FðQÞ j 2 ½1þ nðo;TÞ�w00 ðQ;oÞ; ð3Þ

where ki and kf are the magnitudes of initial and final neutron momentumand F(Q) is the Fe2þ magnetic form factor, and (gre)2¼ 0.2905 barn � sr� 1.

The quantity 2ðgreÞ2pg2m2

Bw00(Q,E) in both superconducting and normal states can

be fitted by a Gaussian AsðnÞe� ½ðqx � 1Þ2

2s2x;sðnÞ

þq2

y2s2

y;sðnÞ�

for resonance wave vector (1,0) and by

cutting the raw data. The outcome is summarized in the Supplementary Table S1,where the unit of E is meV and that of As(n) is mbarn?meV� 1 � sr� 1 � Fe� 1. Forthe case below 5 meV, we assume that An decreases to zero linearly with energy andAs¼An (see Fig. 1h in Zhang et al.18), while the s keeps the value at 5 meV. Theassumption is shown in Supplementary Figure S8, where the resonance is seen atE¼ 15 meV.

Because the condensation energy is only defined at zero temperature, we takeT¼ 0 in the formula equation (3) and the integral gives:

hSi � Siþ xiS �hSi � Siþ xiN¼� 0:0039; hSi � Siþ yiS �hSi � Siþ yiN¼0:0043;

Xl¼x� y

ðhSi � Siþ liS �hSi � Siþ liNÞ¼� 0:0073: ð4Þ

The magnetic exchange coupling constants in an anisotropic model areestimated to be

J1aS¼53:3 meV; J1bS¼� 8:3 meV; J2S¼12:2 meV; ð5Þ

which are 10% smaller than that of BaFe2As2 (ref. 13) and we estimate S to be closeto ½ (ref. 24). Hence the exchange energy change is

DEex¼DXoi;j4

JijhSi � Sji¼� 0:66 meVperFe ð6Þ

The condensation energy Uc for optimally doped Ba0.67K0.33Fe2As2 can becalculated to be

Uc¼� 17:3 J mol� 1¼� 17:31 eV

1:6�10� 19

16:02�1023f :u:

¼� 17:31 eV

1:6�10� 19

12�6:02�1023Fe

¼� 0:09 meVperFeð7Þ

from the specific heat data of Popovich et al.43 Therefore, we have the ratioDEex/UcE7.4, meaning that the change in the magnetic exchange energy issufficient to account for the superconducting condensation energy inBa0.67K0.33Fe2As2.

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AcknowledgementsThe single crystal growth and neutron scattering work at Rice/UTK is supported by theUS DOE BES under Grant No. DE-FG02-05ER46202. Work at IOP is supported by theMOST of China 973 programs (2012CB821400, 2011CBA00110) and NSFC. TheLDAþDMFT computations were made possible by an Oak Ridge leadership computingfacility director discretion allocation to Rutgers. The work at Rutgers is supported byDOE BES DE-FG02-99ER45761 (G.K.) and NSF-DMR 0746395 (K.H.). T.A.M.acknowledges the Center for Nanophase Materials Sciences, which is sponsored at ORNLby the Scientific User Facilities Division, BES, US DOE.

Author contributionsThis paper contains data from three different neutron scattering experiments in thegroup of P.D. lead by M.W. (Ba0.67K0.33Fe2As2), C.Z. (KFe2As2), and X.L. (BaFe1.7-

Ni0.3As2). These authors made equal contributions to the results reported in the paper.For Ba0.67K0.33Fe2As2, M.W., H.L., E.A.G. and P.D. carried out neutron scatteringexperiments. Data analysis was done by M.W. with help from H.L. and E.A.G. Thesamples were grown by C.Z., M.W., Y.S., X.L. and coaligned by M.W. and H.L. RPAcalculation is carried out by T.A.M. The DFT and DMFT calculations were done by Z.Y.,K.H. and G.K. Superconducting condensation energy was estimated by X.Z. For KFe2As2,the samples were grown by C.Z and G.T. Neutron scattering experiments were carriedout by C.Z., E.A.G. and P.D. For BaFe1.7Ni0.3As2, the samples were grown by X.L., H.L.,and coaligned by. X.Y.L. and M.Y.W. Neutron scattering experiments were carried out byX.L., T.G.P. and P.D. The data are analysed by X.L. The paper was written by P.D., M.W.,X.L. and C.L.Z. with input from T.M., K.H. and G.K. All co-authors provided commentson the paper.

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Competing financial interests: The authors declare no competing financial interests.

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How to cite this article: Wang, M. et al. Doping dependence of spin excitations and itscorrelations with high-temperature superconductivity in iron pnictides. Nat. Commun.4:2874 doi: 10.1038/ncomms3874 (2013).

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